K12n877

Dowker-Thistlethwaite code

6 -16 10 20 24 2 18 -4 22 8 12 14

Jones polynomial	[math]\displaystyle{ q^3-5 q^2+12 q-18+24 q^{-1} -26 q^{-2} +25 q^{-3} -21 q^{-4} +14 q^{-5} -7 q^{-6} +2 q^{-7} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^4+7 t^3-20 t^2+32 t-35+32 t^{-1} -20 t^{-2} +7 t^{-3} - t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -z^8-z^6+2 z^4-z^2+1 }[/math]
Determinant	155
Signature	-2
HOMFLY-PT polynomial	[math]\displaystyle{ a^8-z^4 a^6-4 z^2 a^6-3 a^6+2 z^6 a^4+7 z^4 a^4+8 z^2 a^4+4 a^4-z^8 a^2-4 z^6 a^2-6 z^4 a^2-6 z^2 a^2-3 a^2+z^6+2 z^4+z^2+2 }[/math]
Kauffman polynomial	[math]\displaystyle{ 4 a^4 z^{10}+4 a^2 z^{10}+9 a^5 z^9+20 a^3 z^9+11 a z^9+6 a^6 z^8+8 a^4 z^8+13 a^2 z^8+11 z^8+a^7 z^7-22 a^5 z^7-48 a^3 z^7-20 a z^7+5 z^7 a^{-1} -10 a^6 z^6-36 a^4 z^6-51 a^2 z^6+z^6 a^{-2} -24 z^6+7 a^7 z^5+37 a^5 z^5+43 a^3 z^5+5 a z^5-8 z^5 a^{-1} +3 a^8 z^4+20 a^6 z^4+47 a^4 z^4+44 a^2 z^4-z^4 a^{-2} +13 z^4-9 a^7 z^3-25 a^5 z^3-20 a^3 z^3-2 a z^3+2 z^3 a^{-1} -4 a^8 z^2-15 a^6 z^2-24 a^4 z^2-17 a^2 z^2-4 z^2+3 a^7 z+6 a^5 z+4 a^3 z+a z+a^8+3 a^6+4 a^4+3 a^2+2 }[/math]

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